[Baldrick Phd]

Originally Posted by TheRave

The order of mathematics:
http://www.purplemath.com/modules/orderops2.htm

The last example applies directly to this discussion.

Again it explains that 16 ÷ 2(2) is ambiguous.

And then goes on to say:

"The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!"

Originally Posted by 5th Horseman

Only because of the ambiguity of how the original sum was written, the only way to clarify the answer is to write the sum in either of the long forms.

I would never have found this ambiguous until this discussion.

I consider the 2(2) to be bracketed therefore would be worked out first rather than 16/2 x 2.

Worrying that professional maths guys are talking about ambiguity as maths is supposed to be an exact science.


Hawking and Penrose at Cambridge, oops forget all that Blackhole and space/time business, we had a bracket in the wrong place

[munta]

Originally Posted by TheRave

So the answer is 288 or 2.

It completely depends on the interpretation of the priority of juxtaposed values.

The original sum requires clarification before answering completely.

FINISH

DONE

Hopefully we can all agree

Yes, with the caveat that I'm sticking to the answer given by Excel, SQL, IBM Cognos, SPSS & TM1. Since If I disagreed with them then my job would be impossible. And that answer is 288

[John259]

It's 288.

Biffo and Rave - sorry but you are totally wrong, probably because you were taught incorrectly.

2(9+3) is exactly the same as 2 x (9+3), i.e. 2 x 12 = 24 (where x is a multiplication sign). However, with literal numbers it should be written with a multiplication sign. It's only with a letter before the opening bracket that the multiplication sign should be omitted.

BTW it's not an equation and you can't solve it. It's an expression and you evaluate it. It isn't calculus, nor is it A level material. Forty years ago it would have been around the second year of secondary school but that may have changed now.

[Bedlem]

Originally Posted by TheRave

So the answer is 288 or 2.

It completely depends on the interpretation of the priority of juxtaposed values.

The original sum requires clarification before answering completely.

FINISH

DONE

Hopefully we can all agree

Nope, I'm sticking with what I originally said!

I agree that it's ambiguous but just apply a little logic...

What is '2(9 + 3)' on its own? Remove the rest of the equation and what does '2(9 +3)' mean? The fact that it isn't seperated by '2 + (9 + 3)' or '2 * (9 + 3)' or any other arrangement, indicates that '2(9 + 3)' is a single 'a(x + y)' string and, as such, I'd work it out as follows

2(9 + 3)
=>2*9 + 2*3
=>18 + 6
=>24

2(9 + 3) = 24.

Ergo

48 / "2(9 + 3)" = 2 because it isn't seperated like:
48 / 2 + (9 + 3)
48 / 2 * (9 + 3)

or any other such arrangement which would lead to other answers.

[VioletSummers]

Originally Posted by John259

It's 288.

Biffo and Rave - sorry but you are totally wrong, probably because you were taught incorrectly.

2(9+3) is exactly the same as 2 x (9+3), i.e. 2 x 12 = 24 (where x is a multiplication sign). However, with literal numbers it should be written with a multiplication sign. It's only with a letter before the opening bracket that the multiplication sign should be omitted.

BTW it's not an equation and you can't solve it. It's an expression and you evaluate it. It isn't calculus, nor is it A level material. Forty years ago it would have been around the second year of secondary school but that may have changed now.

I still stand by what I say that it's 2. Simple BODMAS - you do the brackets first and that leaves 2.
BIB - Yep, it's around year 8/9 maths, depending on higher or lower sets, so it's not changed.

[VioletSummers]

Originally Posted by Bedlem

Nope, I'm sticking with what I originally said!

I agree that it's ambiguous but just apply a little logic...

What is '2(9 + 3)' on its own? Remove the rest of the equation and what does '2(9 +3)' mean? The fact that it isn't seperated by '2 + (9 + 3)' or '2 * (9 + 3)' or any other arrangement, indicates that '2(9 + 3)' is a single 'a(x + y)' string and, as such, I'd work it out as follows

2(9 + 3)
=>2*9 + 2*3
=>18 + 6
=>24

2(9 + 3) = 24.

Ergo

48 / "2(9 + 3)" = 2 because it isn't seperated like:
48 / 2 + (9 + 3)
48 / 2 * (9 + 3)

or any other such arrangement which would lead to other answers.

THIS! I think Iove you..

God, I'm such a maths nerd

[husted]

The point of brackets is to clarify the expression to make clear what should be done first. But if you have a number outside, then this needs to be operated on everything inside the brackets :
So if you have:
2(9+3)
then this is the same as
2x9 + 2x3.
But this isnt clear, so we write this as :
(2x9) + (2x3)

So a clearer way to put the expression might be

48 ÷ ((2x9) + (2x3))

which equals 2.

[patsylimerick]

7 pages on THIS? It's 2 by the way.

[The 12th Doctor]

It's 2.

[Bedlem]

Originally Posted by VioletSummers

THIS! I think Iove you..

God, I'm such a maths nerd

Hey, it's just my opinion! I dropped out of Maths when I was 15 so understand that I'm 'uneducated' but applying my own logic.

(But yeah, the answer is still 2)

[John259]

Originally Posted by husted

So a clearer way to put the expression might be

48 ÷ ((2x9) + (2x3))

That is wrong, because the 2 is outside the brackets in the original expression, not inside them.

[Biffo the Bear]

Originally Posted by John259

That is wrong, because the 2 is outside the brackets in the original expression, not inside them.

Ah, but it's okay to add a multiplication sign which wasn't there before?

Like I said earlier, if you're going to say:

Well, 2(3+9) is the same as 2*(3+9)

What you should actually be saying is:

Well, 2(3+9) is the same as (2*(3+9))

[VioletSummers]

Originally Posted by husted

The point of brackets is to clarify the expression to make clear what should be done first. But if you have a number outside, then this needs to be operated on everything inside the brackets :
So if you have:
2(9+3)
then this is the same as
2x9 + 2x3.
But this isnt clear, so we write this as :
(2x9) + (2x3)

So a clearer way to put the expression might be

48 ÷ ((2x9) + (2x3))

which equals 2.

Come on people... read this post ^. Husted is right.

Originally Posted by Bedlem

Hey, it's just my opinion! I dropped out of Maths when I was 15 so understand that I'm 'uneducated' but applying my own logic.

(But ye the answer is still 2)

But it matches with what I'm 100% sure is right, so woo!

Originally Posted by John259

That is wrong, because the 2 is outside the brackets in the original expression, not inside them.

Wrong. Numbers outside the brackets affect everything inside them.

[Biffo the Bear]

I think we're seeing an overall victory for 2s here, which is right because logic dictates as thus!

[John259]

Originally Posted by Biffo the Bear

Ah, but it's okay to add a multiplication sign which wasn't there before?

Like I said earlier, if you're going to say:

Well, 2(3+9) is the same as 2*(3+9)

That is correct.

What you should actually be saying is:

Well, 2(3+9) is the same as (2*(3+9))

That is incorrect. Brackets only affect what is inside them.

[lorry]

I'm in the 2 camp!

work out the brackets and its associated number first which is

2 x 12 = 24

then work left to right

48 ÷ 24 = 2

Simples.

[Biffo the Bear]

Originally Posted by John259

Brackets only affect what is inside them.

Or what is cojoined to them, without a multiplication sign separating them.

a(b+c) = (a*(b+c))

[John259]

Originally Posted by Biffo the Bear

Or what is cojoined to them, without a multiplication sign separating them.

a(b+c) = (a*(b+c))

No. Your outer brackets are incorrect.

a(b+c) = ab + ac (the distribution rule) but no outer brackets are implied.

[VioletSummers]

Originally Posted by John259

That is correct.

That is incorrect. Brackets only affect what is inside them.

The numbers outside the brackets affect what's inside them. Numbers in the brackets don't affect anything else, which is why they are in brackets.


BODMAS - Brackets are first.

The 2 is attached to the bracket as no-one has put a multiplication sign there. 2(9+3) = (2x9)+(2x3)=24

48/24=2

[Biffo the Bear]

For the love of God. RIGHT, WHICH ONE OF THESE MAKES SENSE:

48 lamb chops / 2(9+3) butchers
48 lamb chops / 24 butchers
2 each

48 lamb chops / 2(9+3) butchers
48 lamb chops/2 butchers * 12
288 each

[John259]

48÷2(9+3)

= 48 ÷ 2 x 12

= 24 x 12

= 288

In BODMAS, division and multiplication have equal priority and there are no brackets around 2 x 12 so you work left to right.

[VioletSummers]

Originally Posted by John259

48÷2(9+3)

= 48 ÷ 2 x 12

= 24 x 12

= 288

In BODMAS, division and multiplication have equal priority and there are no brackets around 2 x 12 so you work left to right.

But why haven't you calculated the brackets first?

The 2 is NOT separated from the brackets with a multiplcation symbol and therefore must be calculated WITH the brackets.

[AlphaK]

Originally Posted by John259

No. Your outer brackets are incorrect.

a(b+c) = ab + ac (the distribution rule) but no outer brackets are implied.

which would give

48 ÷ 2*9 + 2*3 = neither 288 or 2

[John259]

Originally Posted by VioletSummers

But why haven't you calculated the brackets first?

I have. What's inside the brackets is 9 + 3 which is 12.

The 2 is NOT separated from the brackets with a multiplcation symbol and therefore must be calculated WITH the brackets.

No. I don't know where you're getting that from but it isn't right. There is no such rule.

[VodkaLove]

It is 2.